Inventiones mathematicae

, Volume 163, Issue 1, pp 1-24

First online:

Correlations for pairs of closed geodesics

  • Mark PollicottAffiliated withDepartment of Mathematics, Warwick University
  • , Richard SharpAffiliated withDepartment of Mathematics, University of Manchester

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In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.